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<p>We investigate conditions on an element in a finite-dimensional division ring over its center such that the associated simple extension over the center is a maximal subfield. Specifically, we prove that a simple subfield extension by a value of either a multilinear polynomial in non-commuting variables or a free group-word at a suitable substitution, is a maximal subfield. This is interesting even in the case of characteristic zero, where any finite algebraic field extension is simple.</p>

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Maximal subfields in division algebras generated by images of polynomials

  • 期刊论文

  • 发表日期：

    2026年3月27日

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  • Le Qui Danh,
  • Trinh Thanh Deo

摘要

We investigate conditions on an element in a finite-dimensional division ring over its center such that the associated simple extension over the center is a maximal subfield. Specifically, we prove that a simple subfield extension by a value of either a multilinear polynomial in non-commuting variables or a free group-word at a suitable substitution, is a maximal subfield. This is interesting even in the case of characteristic zero, where any finite algebraic field extension is simple.